p if and only if q
The statement “p if and only if q” is a logical connective used in mathematics and logic, also known as “biconditional” or “equivalence”
The statement “p if and only if q” is a logical connective used in mathematics and logic, also known as “biconditional” or “equivalence”. It means that p and q are both true or both false. The symbol commonly used to represent “if and only if” is ↔ or ≡.
To understand “p if and only if q”, we can break it down into two parts:
1. “p if q”: This means that if q is true, then p must also be true. In other words, q being true is a sufficient condition for p to be true.
2. “p only if q”: This means that if p is true, then q must also be true. In other words, q being true is a necessary condition for p to be true.
Combining these two parts, “p if and only if q” indicates that p and q are completely dependent on each other. If one is true, then the other must be true, and if one is false, then the other must be false as well.
This concept is often used in mathematics to establish equivalence between different statements or conditions. It helps in forming logical arguments, proving theorems, and establishing mathematical relationships.
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